I discovered that the foam is very easy and fun to shape over the stove. Turn the burner up to a high setting, hold the foam section over it for a count of three or so, bend. Lather, rinse, repeat. This can very safely be done with bare hands because the foam never gets too hot to hold. Just don't be a doofus and stick your fingers near the burner. And unless you would like a bumpy texture, try not to grasp the edges with your fingers or you may get fingerprint indentations in the foam. (It's better to use the palms and heels of your hands to squish the part that needs to be bent.) If you do, though, there's help. Mine magically sprung out after another round of heating. w00t.
I tested out the wood glue stiffening method by using duct tape to hold a small strip bent and applying a couple of layers to each side. It really helps the foam keep its shape even though it isn't dry yet. It also dries very smoothly, which may help if you decide to paint the foam instead of gluing on vinyl. Thus, when finished shaping the front and back, I coated the back sides with a nice layer of wood glue.
If you decide to paint this type of armor directly instead of gluing on vinyl, it probably looks best to use a variegated finish like Yui does because the foam does have a texture and it seems pretty difficult to get it super smooth without some sort of over layer. My next step is to get some cheapy craft acrylics of the right color and do paint tests on bare and wood glued foam. I need to see how the paint looks and holds up to flexing. I found online sources for matte purple and metallic gold stretch vinyl should I choose to go that route. I will have to decide which method to use before I attach any collars and trim. If painted, they go on first. If vinyl-wrapped, you need to laminate them before attaching.